One, None or Infinitely Many Solutions
Written by Adi Ackerman, Head Teacher
"One, None or Infinitely Many Solutions" is written for 8th Grade (Ages 13-14), and it covers Common Core 8.EE.C.7.A. A 7th grader who is already steady on algebra can use it too, and an older student can use it as a short review.
8th grade math worksheet: simplify both sides of 12 equations and circle One, None or Many, from 5x + 3 = 5x − 7 to 2(x + 4) = 2x + 8. Answer key included. Part of our number of solutions algebra collection. Aligned to Common Core standards.
How do I use this worksheet?
Use the test values sheet first so students see what a solution is. Then classify, build and sort. The card sort works well with partners.
What students will practice
- Students will simplify both sides of each equation.
- Students will decide whether an equation has one, no or infinitely many solutions.
- Students will classify 12 equations such as −(x − 6) = 6 − x.
Solve Equations by Combining Like Terms First
Combine Like Terms With Negatives, Then Solve
Solve Equations With the Distributive Property
Distribute a Negative Factor, Then Solve
Solve Multi-Step Equations With Fraction Coefficients
Solve Multi-Step Equations With Decimal Coefficients
Multi-Step Equations With Fraction Solutions
Solve Multi-Step Equations and Check Each Answer
Curriculum Links
Common Core State Standards
Expressions and Equations · 8th Grade
Standard: Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
View all 8.EE.C.7.A worksheets →Find this in the curriculum
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FAQ
How do I use this number of solutions worksheet?
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Use the test values sheet first so students see what a solution is. Then classify, build and sort. The card sort works well with partners.
What does this worksheet teach?
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Simplify both sides of 12 equations and circle One, None or Many, from 5x + 3 = 5x − 7 to 2(x + 4) = 2x + 8. The directions on the page read: Simplify both sides. Circle One, None or Many (infinitely many) solutions. An answer key is included.
Can I use this number of solutions worksheet for homeschool or classroom?
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Yes, both. We made it for 8th grade algebra, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.
How do you know if an equation has no solution?
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Simplify both sides. If the x terms cancel and a false statement is left, such as 5x + 3 = 5x − 7 turning into 3 = −7, no value of x works. The equation has no solution.
When does an equation have infinitely many solutions?
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When both sides simplify to the same expression, such as 2(x + 4) = 2x + 8. Every value of x makes it true. The x terms cancel and a true statement like 8 = 8 is left.
How do you check if a value is a solution?
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Substitute the value into each side and find the left and right values. If they are equal, it is a solution. Is It a Solution? Test Values in Equations has 12 equations, some with fraction values such as 5/2.
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Solve Equations by Combining Like Terms First
Combine Like Terms With Negatives, Then Solve
Solve Equations With the Distributive Property
Distribute a Negative Factor, Then Solve
Solve Multi-Step Equations With Fraction Coefficients
Solve Multi-Step Equations With Decimal Coefficients
Multi-Step Equations With Fraction Solutions
Solve Multi-Step Equations and Check Each Answer